Impact of (k,t) sampling on DCE MRI tracer kinetic parameter estimation in digital reference objects

Accelerated model-based T1, T2* and proton density mapping using a Bayesian approach with automatic hyperparameter estimation

PURPOSE

To achieve automatic hyperparameter estimation for the model-based recovery of quantitative MR maps from undersampled data, we propose a Bayesian formulation that incorporates the signal model and sparse priors among multiple image contrasts.

THEORY

We introduce a novel approximate message passing framework "AMP-PE" that enables the automatic and simultaneous recovery of hyperparameters and quantitative maps.

METHODS

We employed the variable-flip-angle method to acquire multi-echo measurements using gradient echo sequence. We explored undersampling schemes to incorporate complementary sampling patterns across different flip angles and echo times. We further compared AMP-PE with conventional compressed sensing approaches such as thel 1 $$ {l}_1 $$ -norm minimization, PICS and other model-based approaches such as GraSP, MOBA.

RESULTS

Compared to conventional compressed sensing approaches such as thel 1 $$ {l}_1 $$ -norm minimization and PICS, AMP-PE achieved superior reconstruction performance with lower errors inT 2 ∗ $$ {\mathrm{T}}_2^{\ast } $$ mapping and comparable performance inT 1 $$ {\mathrm{T}}_1 $$ and proton density mappings. When compared to other model-based approaches including GraSP and MOBA, AMP-PE exhibited greater robustness and outperformed GraSP in reconstruction error. AMP-PE offers faster speed than MOBA. AMP-PE performed better than MOBA at higher sampling rates and worse than MOBA at a lower sampling rate. Notably, AMP-PE eliminates the need for hyperparameter tuning, which is a requisite for all the other approaches.

CONCLUSION

AMP-PE offers the benefits of model-based recovery with the additional key advantage of automatic hyperparameter estimation. It works adeptly in situations where ground-truth is difficult to obtain and in clinical environments where it is desirable to automatically adapt hyperparameters to individual protocol, scanner and patient.

Optimizing pseudo-spiral sampling for abdominal DCE MRI using a digital anthropomorphic phantom

PURPOSE

For reliable DCE MRI parameter estimation, k-space undersampling is essential to meet resolution, coverage, and signal-to-noise requirements. Pseudo-spiral (PS) sampling achieves this by sampling k-space on a Cartesian grid following a spiral trajectory. The goal was to optimize PS k-space sampling patterns for abdomin al DCE MRI.

METHODS

The optimal PS k-space sampling pattern was determined using an anthropomorphic digital phantom. Contrast agent inflow was simulated in the liver, spleen, pancreas, and pancreatic ductal adenocarcinoma (PDAC). A total of 704 variable sampling and reconstruction approaches were created using three algorithms using different parametrizations to control sampling density, halfscan and compressed sensing regularization. The sampling patterns were evaluated based on image quality scores and the accuracy and precision of the DCE pharmacokinetic parameters. The best and worst strategies were assessed in vivo in five healthy volunteers without contrast agent administration. The best strategy was tested in a DCE scan of a PDAC patient.

RESULTS

The best PS reconstruction was found to be PS-diffuse based, with quadratic distribution of readouts on a spiral, without random shuffling, halfscan factor of 0.8, and total variation regularization of 0.05 in the spatial and temporal domains. The best scoring strategy showed sharper images with less prominent artifacts in healthy volunteers compared to the worst strategy. Our suggested DCE sampling strategy also showed high quality DCE images in the PDAC patient.

CONCLUSION

Using an anthropomorphic digital phantom, we identified an optimal PS sampling strategy for abdominal DCE MRI, and demonstrated feasibility in a PDAC patient.

Digital reference object toolkit of breast DCE MRI for quantitative evaluation of image reconstruction and analysis methods

PURPOSE

To develop a digital reference object (DRO) toolkit to generate realistic breast DCE-MRI data for quantitative assessment of image reconstruction and data analysis methods.

METHODS

A simulation framework in a form of DRO toolkit has been developed using the ultrafast and conventional breast DCE-MRI data of 53 women with malignant (n = 25) or benign (n = 28) lesions. We segmented five anatomical regions and performed pharmacokinetic analysis to determine the ranges of pharmacokinetic parameters for each segmented region. A database of the segmentations and their pharmacokinetic parameters is included in the DRO toolkit that can generate a large number of realistic breast DCE-MRI data. We provide two potential examples for our DRO toolkit: assessing the accuracy of an image reconstruction method using undersampled simulated radial k-space data and assessing the impact of theB 1 + $$ {\mathrm{B}}_1^{+} $$ field inhomogeneity on estimated parameters.

RESULTS

The estimated pharmacokinetic parameters for each region showed agreement with previously reported values. For the assessment of the reconstruction method, it was found that the temporal regularization resulted in significant underestimation of estimated parameters by up to 57% and 10% with the weighting factor λ = 0.1 and 0.01, respectively. We also demonstrated that spatial discrepancy ofv p $$ {v}_p $$ andPS $$ \mathrm{PS} $$ increase to about 33% and 51% without correction forB 1 + $$ {\mathrm{B}}_1^{+} $$ field.

CONCLUSION

We have developed a DRO toolkit that includes realistic morphology of tumor lesions along with the expected pharmacokinetic parameter ranges. This simulation framework can generate many images for quantitative assessment of DCE-MRI reconstruction and analysis methods.

Feasibility of measuring blood-brain barrier permeability using ultra-short echo time radial magnetic resonance imaging

BACKGROUND AND PURPOSE

The purpose of this study is to evaluate the feasibility of using 3-dimensional (3D) ultra-short echo time (UTE) radial imaging method for measurement of the permeability of the blood-brain barrier (BBB) to gadolinium-based contrast agent. In this study, we propose to use the golden-angle radial sparse parallel (GRASP) method with 3D center-out trajectories for UTE, hence named as 3D UTE-GRASP. We first examined the feasibility of using 3D UTE-GRASP dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) for differentiating subtle BBB disruptions induced by focused ultrasound (FUS). Then, we examined the BBB permeability changes in Alzheimer's disease (AD) pathology using Alzheimer's disease transgenic mice (5xFAD) at different ages.

METHODS

For FUS experiments, we used four Sprague Dawley rats at similar ages where we compared BBB permeability of each rat receiving the FUS sonication with different acoustic power (0.4-1.0 MPa). For AD transgenic mice experiments, we included three 5xFAD mice (6, 12, and 16 months old) and three wild-type mice (4, 8, and 12 months old).

RESULTS

The result from FUS experiments showed a progressive increase in BBB permeability with increase of acoustic power (p < .05), demonstrating the sensitivity of DCE-MRI method for detecting subtle changes in BBB disruption. Our AD transgenic mice experiments suggest an early BBB disruption in 5xFAD mice, which is further impaired with aging.

CONCLUSION

The results in this study substantiate the feasibility of using the proposed 3D UTE-GRASP method for detecting subtle BBB permeability changes expected in neurodegenerative diseases, such as AD.

Open source code for the generation of digital reference objects for dynamic contrast-enhanced MRI analysis software validation

OBJECTIVES

Dynamic contrast-enhanced MR images can be analyzed through the application of a wide range of kinetic models. This process is prone to variability and a lack of standardization that can affect the measured metrics. There is a need for customized digital reference objects (DROs) for the validation of DCE-MRI software packages that undertake kinetic model analysis. DROs are currently available only for a small subset of the kinetic models commonly applied to DCE-MRI data. This work aimed to address this gap.

METHODS

Code was written in the MATLAB programming environment to generate customizable DROs. This modular code allows the insertion of a plug-in to describe the kinetic model to be tested. We input our generated DROs into three commercial and open-source analysis packages and assessed the agreement of kinetic model parameter values output with the 'ground-truth' values used in the DRO generation.

RESULTS

For the five kinetic models tested, the concordance correlation coefficient values were >98%, indicating excellent agreement of the results with 'ground-truth'.

CONCLUSIONS

Testing our DROs on three independent software packages produced concordant results, strongly suggesting our DRO generation code is correct. This implies that our DROs can be used to validate other third party software for the kinetic model analysis of DCE-MRI data.

ADVANCES IN KNOWLEDGE

This work extends published work of others to allow customized generation of test objects for any applied kinetic model and allows the incorporation of B1 mapping into the DRO for application at higher field strengths.

Model-constrained reconstruction accelerated with Fourier-based undersampling for hyperpolarized [1-13 C] pyruvate imaging

PURPOSE

Model-constrained reconstruction with Fourier-based undersampling (MoReFUn) is introduced to accelerate the acquisition of dynamic MRI using hyperpolarized [1-13 C]-pyruvate.

METHODS

The MoReFUn method resolves spatial aliasing using constraints introduced by a pharmacokinetic model that describes the signal evolution of both pyruvate and lactate. Acceleration was evaluated on three single-channel data sets: a numerical digital phantom that is used to validate the accuracy of reconstruction and model parameter restoration under various SNR and undersampling ratios, prospectively and retrospectively sampled data of an in vitro dynamic multispectral phantom, and retrospectively undersampled imaging data from a prostate cancer patient to test the fidelity of reconstructed metabolite time series.

RESULTS

All three data sets showed successful reconstruction using MoReFUn. In simulation and retrospective phantom data, the restored time series of pyruvate and lactate maintained the image details, and the mean square residual error of the accelerated reconstruction increased only slightly (< 10%) at a reduction factor up to 8. In prostate data, the quantitative estimation of the conversion-rate constant of pyruvate to lactate was achieved with high accuracy of less than 10% error at a reduction factor of 2 compared with the conversion rate derived from unaccelerated data.

CONCLUSION

The MoReFUn technique can be used as an effective and reliable imaging acceleration method for metabolic imaging using hyperpolarized [1-13 C]-pyruvate.

Joint Optimization of k-t Sampling Pattern and Reconstruction of DCE MRI for Pharmacokinetic Parameter Estimation

This work proposes to develop and evaluate a deep learning framework that jointly optimizes k-t sampling patterns and reconstruction for head and neck dynamic contrast-enhanced (DCE) MRI aiming to reduce bias and uncertainty of pharmacokinetic (PK) parameter estimation. 2D Cartesian phase encoding k-space subsampling patterns for a 3D spoiled gradient recalled echo (SPGR) sequence along a time course of DCE MRI were jointly optimized in a deep learning-based dynamic MRI reconstruction network by a loss function concerning both reconstruction image quality and PK parameter estimation accuracy. During training, temporal k-space data sharing scheme was optimized as well. The proposed method was trained and tested by multi-coil complex digital reference objects of DCE images (mcDROs). The PK parameters estimated by the proposed method were compared with two published iterative DCE MRI reconstruction schemes using normalized root mean squared errors (NRMSEs) and Bland-Altman analysis at temporal resolutions of [Formula: see text] = 2s, 3s, 4s, and 5s, which correspond to undersampling rates of R = 50, 34, 25, and 20. The proposed method achieved low PK parameter NRMSEs at all four temporal resolutions compared with the benchmark methods on testing mcDROs. The Bland-Altman plots demonstrated that the proposed method reduced PK parameter estimation bias and uncertainty in tumor regions at temporal resolution of 2s. The proposed method also showed robustness to contrast arrival timing variations across patients. This work provides a potential way to increase PK parameter estimation accuracy and precision, and thus facilitate the clinical translation of DCE MRI.

Dynamic contrast-enhanced MRI parametric mapping using high spatiotemporal resolution Golden-angle RAdial Sparse Parallel MRI and iterative joint estimation of the arterial input function and pharmacokinetic parameters

The aim of this work is to develop a data-driven quantitative dynamic contrast-enhanced (DCE) MRI technique using Golden-angle RAdial Sparse Parallel (GRASP) MRI with high spatial resolution and high flexible temporal resolution and pharmacokinetic (PK) analysis with an arterial input function (AIF) estimated directly from the data obtained from each patient. DCE-MRI was performed on 13 patients with gynecological malignancy using a 3-T MRI scanner with a single continuous golden-angle stack-of-stars acquisition and image reconstruction with two temporal resolutions, by exploiting a unique feature in GRASP that reconstructs acquired data with user-defined temporal resolution. Joint estimation of the AIF (both AIF shape and delay) and PK parameters was performed with an iterative algorithm that alternates between AIF and PK estimation. Computer simulations were performed to determine the accuracy (expressed as percentage error [PE]) and precision of the estimated parameters. PK parameters (volume transfer constant [K^trans ], fractional volume of the extravascular extracellular space [v_e ], and blood plasma volume fraction [v_p ]) and normalized root-mean-square error [nRMSE] (%) of the fitting errors for the tumor contrast kinetic data were measured both with population-averaged and data-driven AIFs. On patient data, the Wilcoxon signed-rank test was performed to compare nRMSE. Simulations demonstrated that GRASP image reconstruction with a temporal resolution of 1 s/frame for AIF estimation and 5 s/frame for PK analysis resulted in an absolute PE of less than 5% in the estimation of K^trans and v_e , and less than 11% in the estimation of v_p . The nRMSE (mean ± SD) for the dual temporal resolution image reconstruction and data-driven AIF was 0.16 ± 0.04 compared with 0.27 ± 0.10 (p < 0.001) with 1 s/frame using population-averaged AIF, and 0.23 ± 0.07 with 5 s/frame using population-averaged AIF (p < 0.001). We conclude that DCE-MRI data acquired and reconstructed with the GRASP technique at dual temporal resolution can successfully be applied to jointly estimate the AIF and PK parameters from a single acquisition resulting in data-driven AIFs and voxelwise PK parametric maps.

An Anthropomorphic Digital Reference Object (DRO) for Simulation and Analysis of Breast DCE MRI Techniques

Advances in accelerated magnetic resonance imaging (MRI) continue to push the bounds on achievable spatial and temporal resolution while maintaining a clinically acceptable image quality. Validation tools, including numerical simulations, are needed to characterize the repeatability and reproducibility of such methods for use in quantitative imaging applications. We describe the development of a simulation framework for analyzing and optimizing accelerated MRI acquisition and reconstruction techniques used in dynamic contrast enhanced (DCE) breast imaging. The simulation framework, in the form of a digital reference object (DRO), consists of four modules that control different aspects of the simulation, including the appearance and physiological behavior of the breast tissue as well as the MRI acquisition settings, to produce simulated k-space data for a DCE breast exam. The DRO design and functionality are described along with simulation examples provided to show potential applications of the DRO. The included simulation results demonstrate the ability of the DRO to simulate a variety of effects including the creation of simulated lesions, tissue enhancement modeled by the generalized kinetic model, T1-relaxation, fat signal precession and saturation, acquisition SNR, and changes in temporal resolution.

Sparse precontrast T1 mapping for high-resolution whole-brain DCE-MRI

PURPOSE

To develop and evaluate an efficient precontrast T₁ mapping technique suitable for quantitative high-resolution whole-brain dynamic contrast-enhanced-magnetic resonance imaging (DCE-MRI).

METHODS

Variable flip angle (VFA) T₁ mapping was considered that provides 1 × 1 × 2 mm³ resolution to match a recent high-resolution whole-brain DCE-MRI protocol. Seven FAs were logarithmically spaced from 1.5° to 15°. T₁ and M₀ maps were estimated using model-based reconstruction. This approach was evaluated using an anatomically realistic brain tumor digital reference object (DRO) with noise-mimicking 3T neuroimaging and fully sampled data acquired from one healthy volunteer. Methods were also applied on fourfold prospectively undersampled VFA data from 13 patients with high-grade gliomas.

RESULTS

T₁ -mapping precision decreased with undersampling factor R, althoughwhereas bias remained small before a critical R. In the noiseless DRO, T₁ bias was <25 ms in white matter (WM) and <11 ms in brain tumor (BT). T₁ standard deviation (SD) was <119.5 ms in WM (coefficient of variation [COV] ~11.0%) and <253.2 ms in BT (COV ~12.7%). In the noisy DRO, T₁ bias was <50 ms in WM and <30 ms in BT. For R ≤ 10, T₁ SD was <107.1 ms in WM (COV ~9.9%) and <240.9 ms in BT (COV ~12.1%). In the healthy subject, T₁ bias was <30 ms for R ≤ 16. At R = 4, T₁ SD was 171.4 ms (COV ~13.0%). In the prospective brain tumor study, T₁ values were consistent with literature values in WM and BT.

CONCLUSION

High-resolution whole-brain VFA T₁ mapping is feasible with sparse sampling, supporting its use for quantitative DCE-MRI.

Impact of (k,t) sampling on DCE MRI tracer kinetic parameter estimation in digital reference objects

Purpose

To evaluate the impact of (k,t) data sampling on the variance of tracer‐kinetic parameter (TK) estimation in high‐resolution whole‐brain dynamic contrast enhanced magnetic resonance imaging (DCE‐MRI) using digital reference objects. We study this in the context of TK model constraints, and in the absence of other constraints.

Methods

Three anatomically and physiologically realistic brain‐tumor digital reference objects were generated. Data sampling strategies included uniform and variable density; zone‐based, lattice, pseudo‐random, and pseudo‐radial; with 50‐time frames and 4‐fold to 25‐fold undersampling. In all cases, we assume a fully sampled first time frame, and prior knowledge of the arterial input function. TK parameters were estimated by indirect estimation (i.e., image‐time‐series reconstruction followed by model fitting), and direct estimation from the under‐sampled data. We evaluated methods based on the Cramér‐Rao bound and Monte‐Carlo simulations, over the range of signal‐to‐noise ratio (SNR) seen in clinical brain DCE‐MRI.

Results

Lattice‐based sampling provided the lowest SDs, followed by pseudo‐random, pseudo‐radial, and zone‐based. This ranking was consistent for the Patlak and extended Tofts model. Pseudo‐random sampling resulted in 19% higher averaged SD compared to lattice‐based sampling. Zone‐based sampling resulted in substantially higher SD at undersampling factors above 10. CRB analysis showed only a small difference between uniform and variable density for both lattice‐based and pseudo‐random sampling up to undersampling factors of 25.

Conclusion

Lattice sampling provided the lowest SDs, although the differences between sampling schemes were not substantial at low undersampling factors. The differences between lattice‐based and pseudo‐random sampling strategies with both uniform and variable density were within the range of error induced by other sources, at up to 25‐fold undersampling.